Can I transpose along a single axis and have the other frames in between move accordingly without damaging the animation
Use the graph editor, F-Curve View.

First select all Bones (Pose Mode) and all Objects (Armature in Object Mode) in the scene you want to manipulate, so that you see all Channels in the Left Panel of the Editor.

Then mark all Keys you want to move (e.g. Select -> After Current Frame)
Now you can move the keyframes with "G" and "X" on the X Axis (unit 1 is one frame).
ATTENTION! Ensure that no channel is marked as "not visible" (Eye closed)


If you want to move all keyframes of the scene, so turn off the Selection "Only include channels relating to selected objects and data"